String sizing is the first step in designing the PV array. It is primarily about matching string voltages to the inverter input operating window. This has long-reaching effects on the whole solar energy system, from the ease of installation, labor and material costs, and performance.
In determining the optimum number of modules in a string, there are actually three inverter input parameters that we should meet with our array voltages:
· Minimum Input Voltage – this is the minimum input voltage that must be met before the inverter starts to get DC power from the PV array for conversion to AC. The whole system will stop producing power once the array voltage goes lower than this value. This is a common cause of performance issues for solar systems. The PV array’s operating voltage, even if designed by a solar PV engineer, can go below this minimum input voltage if he has failed to consider the effect of temperature on PV module voltages. Another reason why PV strings sometimes fail to meet the minimum input voltage is when the grid voltage increases by a percentage, the minimum input voltage also increases by the same percentage. Other than these reasons, the PV modules also degrade over time, usually around 0.8% of the rated power per year. This corresponds to an estimated voltage loss of 0.4% per year or 10% over the course of its 25-year lifespan.
· Maximum Input Voltage – this determines the maximum DC voltage that the PV array can have. The inverter can be damaged if exposed to voltages higher than this value. A common cause of overvoltage to the inverter is mistakenly putting two strings in series rather than in parallel. Similar to the minimum input voltage, the PV array can also accidentally go above this maximum input voltage if the solar PV engineer fails to consider temperature effects. PV modules’ voltage increases with decreasing temperature. In most cases, the temperature variation from standard temperature (25OC) to the lowest site temperature is much more than the variation to the highest site temperature, especially for locations that experience winter. This means that the effect of voltage increase due to decreasing temperature will be much more than the effect of voltage decrease due to increasing temperature.
· MPP Voltage Range – this is the voltage range of the string in which the inverter can track the MPP of the PV modules. Fortunately for designers, if the string is designed so that its operating voltage will always be within the maximum and minimum input voltages, its VMPP will also most likely fall in the MPP voltage range.
Case Study: DC Voltage Calculations in String Sizing
This case study illustrates the step by step process in string sizing for solar energy systems.
Location: Springfield, Massachusetts.
PV module: Yingli YL230P-29b, 230 W STC, 29.5 VMP, 7.8 IMP, 37.0 VOC, 8.4 ISC, -0.137 V/°C temperature coefficient of VOC (-0.37%/°C x 37.0 VOC), -0.133 V/°C temperature coefficient of VMP (based on the published temperature coefficient for Pmp, -0.45%/°C x 29.5 VMP).
Inverter: SMA STP25000-TL, 25 kW, 1,000 Vdc maximum input, 188V start input voltage.
We first need to determine the highest and lowest expected temperature in our location. We can get this data from NASA’s web mapping application, POWER. This can be accessed on this link: https://power.larc.nasa.gov/.
Scroll down to the Multiple Data Access Options part and click on Power Data Access Viewer:
On Choose a User Community, just keep it at SSE-Renewable Energy.
On Choose a Temporal Average, choose Climatology.
On Enter Lat/Lon or Add a Point to Map, you can point the location on the map or enter the location’s latitude and longitude.
The Select Time Extent Part is not needed.
Keep ASCII selected on the Select Output File Formats.
Scroll down on the POWER Single Point Data Access window to number 6, Select Parameters. Double click on the Meteorology (Temperature) folder to expand it and check on Maximum and Minimum Temperatures at 2 meters.
On the bottom of this window, click Submit.
It will take you to another window. On the Output files, click ASCII.
It will open another tab that looks like the one shown below. We will be able to see on the bottom part, the maximum and minimum expected temperatures for each month. On this site, our lowest expected temperature is -10.08OC which will occur in January while the highest is 26.82OC in August.
Maximum modules in series – to determine the maximum number of PV modules in series, first calculate the per-module maximum voltage as follows:
where: αVOC = temperature coefficient of VOC
For our example:
VMAX = 37.0V + ((-10.08OC - 25OC) * -0.37%/ OC)
= 37.0V + ((-35.08OC) * -0.37%/ OC)
= 37.0V + (12.9796%)
This means that our VOC of 37.0V will be increased by 12.9796%. This is equivalent to 4.8V.
= 37.0V + 4.8V
VMAX = 41.8V
Then, divide the maximum inverter input voltage by the temperature-corrected open-circuit voltage and round down to the nearest whole number to determine the maximum number of PV modules in series.
NMAX = 1,000V/41.8V
NMAX = 23 PV modules in series.
Minimum modules in series – To determine the minimum number of PV modules in series, first calculate the per module minimum voltage as follows:
where: βVMP = temperature coefficient of VMP
Take note that not every PV module datasheet indicates a separate temperature coefficient for VMP.
For our example:
VMIN = 29.5V + ((26.82OC - 25OC) * -0.45%/ OC)
= 29.5V + ((1.82OC) * -0.45%/ OC)
= 29.5V + (-0.819%)
= 29.5V – 0.24V
VMIN = 29.26V
Select and apply a multiplier to account for the combined effects of high ac grid voltage, array degradation, and module voltage tolerance. 0.85 is used in this case:
VMIN = 29.26V * 0.85
VMIN = 24.871V
Then, divide the start input voltage by the minimum voltage per PV module and round up to the nearest whole number to determine the minimum number of PV modules in series. If this parameter is not given in the inverter datasheet, the minimum MPPT voltage is used instead:
NMIN = 188V/24.871V
So for our example, the acceptable number of PV modules in a string ranges from 8 to 23. In practice, it is always more advisable to put more PV modules in a string. However, we may not always be able to choose to put the maximum allowable number of PV modules in a string because of physical limitations. For example, if we can fit only 40 PV modules on one roof segment, it will be better to divide it into two strings of 20 PV modules each.
PV Array Sizing Ratio
A PV module only produces its maximum rated power during standard test conditions (STC) of having an irradiance input of 1,000W/m2 and a cell temperature of 25OC. In actual operations, however, these conditions are rarely met. Because of this, the inverter also rarely operates at full capacity. Also, there are wiring losses from the PV modules to the inverter, which further reduces the total energy that reaches the inverter input. This is a graph of a sample hourly solar PV production with respect to the maximum inverter capacity:
In this graph, the white bars represent the energy production of the solar panels without losses while the blue bars represent the energy production after subtracting the losses. The red line is the inverter capacity. This graph is for a 1:1 PV array sizing ratio, with a 1kW PV array and a 1kW inverter.
During the mornings and afternoons, there is more input solar PV power, so the inverter operates much closer to its maximum capacity at the expense of having some excess unused solar PV power during noontime. Not only that more of the inverter capacity is utilized, but more energy is also now available to the inverter input which translates to an increase in total energy output.
However, there is a limit to increasing the PV array capacity being beneficial. The optimal PV array to inverter capacity ratio, or what is called DC to AC sizing ratio, is around 1.25. Further increases in the sizing ratio give lower and lower increases in the total energy output.
In practice, it is a common design principle to set the DC to AC sizing ratio as close as possible to 1.25. For PV arrays that are not in the optimum tilt and orientation, we can set a higher sizing ratio (as much as 1.35), as these arrays will produce less than optimum energy yields. Some available solar PV simulation software in the market can be used to further analyze how much we can increase the sizing ratio.
Solar/PV Array Roof Placement
In choosing where to place PV modules on the roof, there are some considerations that must be made:
Maximum solar PV production – in roof-mounted applications, however, we have limited options in choosing these parameters. To illustrate this point, kindly see this Google Earth image of a residential house shown below:
In this case, we have 4 different roof segments with four different orientations, labeled A to D. When it comes to the tilt angle, we don’t have this choice as we are limited to the tilt angle of the roof itself. To maximize solar PV production, we will have to choose which roof segment is closest to the optimum. Remember that the optimum orientation is one that is pointed towards the equator (South for those located in the northern hemisphere and vice versa). In this example, which is located in the Philippines (northern hemisphere), the best roof segment to put PV modules on is roof segment C.
Shading and obstructions – in the design process, the solar PV engineer must already be able to identify possible shading instances on the roof caused by electric poles, trees, chimneys, etc. A general guideline is to set an offset distance from possible causes of shading to where you start putting PV modules to minimize its effect. We will discuss further on how to model the effects of shading using Google Sketchup on the next chapter.
String allocation to inverter MPPT inputs – the number of MPPT inputs that the inverter has must always be considered in choosing which roof/s to put the PV modules on. The general rule is that all strings of PV modules installed on one roof orientation should be connected to the same MPPT inputs. Two or more strings on different roof orientations will suffer severely in their energy productions. Different roof orientations will always receive different amounts of irradiance and thus, different PV module strings placed on these will always have different MPPs. When PV modules on different roof orientations are connected on only one MPPT input, they will be forced to operate on a voltage and current which maximizes the production for all strings while individual strings are not operating at their individual MPPs.
DC Combiner Boxes and String Fuses
A DC combiner box, as its name suggests, “combines” several PV module string outputs into one pair of conductors. It is a box in which several input conductors come together into a common bus with a single pair of output conductors. DC combiner boxes also usually have provisions for an overcurrent protection device (OCPD) on each of the input conductors, internal dc disconnect switch on the output conductor, surge protection devices, or monitoring equipment.
DC combiner boxes are used in solar energy systems for larger inverters (mostly central inverters), which has fewer input connectors than the number of strings usually used with it. For example, the SMA STP60, a 60kW string inverter only has one input connector. It is usually used with a combiner box to combine all solar PV string inputs into one pair of conductors which is suitable for its input configuration.
DC combiner boxes also provide a location for a disconnecting device to isolate and de-energize the PV module strings to the PV wire that serves as the input to the inverter during troubleshooting and maintenance activities.
Another function of the DC combiner box is that it provides a location for OCPDs, which are usually in the form of string fuses. Because of this, DC combiner boxes for solar PV applications have string fuses for every input connection. These string fuses are housed in fuse holders with a pull out carrier for easy replacement.
The PV wires connected to the PV module strings are designed to withstand 1.56 times the PV module’s ISC or short-circuit current. The inverter, on the other hand, usually also comes with an internal OCPD on its input. Fuses are usually used to protect the wires and the equipment from short-circuit currents, but in this case, both the PV wires and the inverter can withstand the short-circuit current from the PV module strings. What then, is the string fuse’s function?
The string fuses used in solar applications are not used to protect the PV wires nor the inverter. What they really protect are the PV module strings themselves. To illustrate this, let us look at a scenario where there are three strings of PV modules connected in parallel. A fault in one of the strings can cause the faulted string to appear as a short-circuit to the other two strings in parallel. When this happens, two times the short-circuit current will flow to the faulted string. This amount of current can damage the PV wires and the PV modules. However, if there is a string fuse in all three PV module strings, this fault current would blow the string fuse on the faulted string, protecting it from damage.
If there are only two strings on this example, the fault current that would flow on the faulted string will only be equal to the short-circuit current of the other string. Both the PV wires and the PV modules themselves would be able to withstand this, and thus, a string fuse will not be necessary anymore. Therefore, as a rule, string fuses are only required on PV arrays with three or more strings connected in parallel.
Shading and Obstructions
There are many possible sources of shading in an actual solar energy system installation, including trees, electrical poles, and nearby tall structures, other roof segments, chimneys, roof ventilators and refrigeration and other roof equipment for flat commercial roofs.
On a site visit, the effects of shading can be analyzed using a Solar Pathfinder. It is a device that can let you get an idea of how much shading a certain obstruction can cause and during which times of the month and hours of the day it will occur.
Without this device, however, we still have a way of analyzing the shading effects of obstructions, which is through Google Sketchup.
Modeling Shading Using Google Sketchup
We can do a shading analysis using Google’s 3d modeling software, Google Sketchup. This software can easily be used by everybody, even those without experience with AutoCAD and other related drawing software because of its very simple commands and interface.
To start our shading analysis, open Google Sketchup:
Our first step would be to set the location for our drawing. First, make sure that we can see the Location toolbar. Go to View Toolbars Click the Location checkbox. The Location toolbar looks like this:
Click on the Add Location button. The Add Location window will appear:
Type the address of the house or building in which you want to do shading analysis on and click Select Region.
Draw the house or building on the part of the map where it is located and the obstructions. Take note that your drawing does not have to be very detailed. Your drawing can be as simple as this:
We now just have to turn on the shadows using the Shadows toolbar. Go to View then Toolbars then Click the Shadows checkbox. The Shadows toolbar looks like this:
Click on the Show/Hide Shadows button to turn on shadows. The two bars on the right side of this button are for the date/month and the time of the day, respectively.
With the shadows on, we will be able to see which parts of the roof will be shaded and when this will happen. The general rule is that we want to avoid shading to our PV modules from 9:00 AM up to 3:00 PM. Set the time on the Shadows toolbar on 9:00 AM and scroll the date/month bar from J (January) to D (December). Repeat this process for 3:00 PM. The largest amounts of shading from 9:00 AM and 3:00 PM should be your basis in determining which parts of the roof you should avoid putting PV modules on.
Solar Farm Array Design:
Solar farms are usually installed on open land. Along with the disadvantage of also having to install additional mounting structures comes the advantage of being able to control these solar array parameters:
Tilt – solar farm array design often starts with determining the optimum tilt and orientation for the site. Unlike rooftop solar arrays where we are confined to the roof’s tilt and orientation, we are free to set these parameters for solar farm arrays through our own mounting system. Remember that the optimum tilt for PV modules is equal to the location’s latitude. However, high tilt angles also increase the required row to row spacing to avoid shading and thus, reduces the total number of PV modules that can be installed on a limited land area. Setting the right tilt angle with respect to the PV module’s performance and the row to row spacing, therefore, becomes an important design decision.
Orientation – similar to the tilt angle of the PV modules, for solar farm arrays, we are free to set this parameter. The optimum orientation for PV modules is due South for locations in the northern hemisphere and vice versa. For lands that are not oriented directly north or South, however, sometimes it is better to point the solar farm array to the orientation of the land for convenience in installation and to have a “cleaner” array layout.